Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×H(3,𝔽4) ⋊ C4 |
| Sylow | C5 ⋊ #12753 |
936 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^2,e^b=egh,f^b=fg,d^c=dg,i^c=i^4,e^d=eh,f^d=fh,i^f=i^453 conjugacy classes — view the full character table.
| maximal subgroup of | #72221414, #72221422 |
| maximal normal subgroup of | #72221422 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096539);